WASHINGTON (AP) — Mitt Romney says Barack Obama doesn't think entrepreneurs built their businesses. The problem is that's not what the president said.

The brouhaha over Obama's comments on small-business success shows no sign of fading and the president pushed back hard with new ads scheduled to run in Virginia, North Carolina, Florida, Ohio, Iowa and Nevada in which the president directly counters Romney's claims. Romney and his allies continue to hammer Obama for comments taken wildly out of context, pummeling the president as a government-obsessed figure who thinks Washington gets the credit for the success of small businesses.

That was not Obama's point when he spoke in Virginia on July 13 about the government's supportive role in providing a stable environment in which businesses can thrive. Nor was it Romney's point when he used similar phrasing in 2002 about Olympic athletes who benefited from supportive parents and coaches.

But in a campaign that makes facts secondary to a good attack, the context doesn't seem to matter.

"Those ads taking my words about small business out of context? They're flat out wrong," Obama says, looking into the camera and addressing voters in the 30-second ad. "Of course Americans build their own businesses."

That is a tidier version of what Obama offered in Virginia.

"Look, if you've been successful, you didn't get there on your own. You didn't get there on your own," Obama said then. "I'm always struck by people who think, 'Well, it must be because I was just so smart.' There are a lot of smart people out there. 'It must be because I worked harder than everybody else.' Let me tell you something: There are a whole bunch of hardworking people out there. If you were successful, somebody along the line gave you some help."

Obama cited teachers and mentors who helped "create this unbelievable American system that we have that allowed you to thrive. Somebody invested in roads and bridges."

Then, Obama teed up the line that left Republicans giddy. "If you've got a business, you didn't build that. Somebody else made that happen. The Internet didn't get invented on its own. Government research created the Internet so that all the companies could make money off the Internet," Obama said, returning to his thesis.

"The point is, is that when we succeed, we succeed because of our individual initiative, but also because we do things together."

Romney and his allies pounced on the "you didn't build that" portion and ignored the rest.

"Well, just read the whole speech. I found the speech even more disconcerting than just that particular line. The context is worse than the quote," Romney told CNBC on Monday.

"I cannot believe the president of the United States could say that I have not made this," one small-business owner says in a web video released Tuesday by American Crossroads, an independent group supporting Romney's campaign.

"When President Obama said in Roanoke that 'if you've got a business you didn't build that, somebody else made that happen,' I was personally extremely insulted," office supplier Melissa Ball of Richmond, Va., said on a Republican Party conference call with reporters.

Recognizing the potency of this theme, the Obama campaign began pushing back harder.

Speaking to about 1,000 donors in Portland, Ore., on Tuesday, Obama accused Romney of "twisting my words around to suggest that I don't value small business."

"Those are the games that are played in campaigns," he added. "Although I have to say, when people omit entire sentences from a speech and they start splicing and dicing, they may have tipped a little bit over their skis. They may have gone over the edge here."

The Obama campaign also released Web videos Monday and Tuesday rebutting Romney's assertions.

In one, the campaign accused the presumptive GOP nominee of having "deliberately altered the meaning of the president's words." A second video out Tuesday featured deputy campaign manager Stephanie Cutter, who said Romney was "not telling the truth about what the president said."

Taken as a whole, Obama's remarks aren't that different from Romney's comments in 2002 to Olympic athletes.

"You Olympians, however, know you didn't get here solely on your own power," Romney said after congratulating the athletes. "For most of you, loving parents, sisters or brothers, encouraged your hopes, coaches guided, communities built venues in order to organize competitions. All Olympians stand on the shoulders of those who lifted them."

Romney's team didn't seem to mind the risk. The backdrop for his campaign stop Monday in California: a blue banner that said, "We Did Build It!"